Because domain geometry is dictated by the volume fraction of the block constituting it, an ABC linear triblock copolymer with unequal volume fractions of A and C blocks can form asymmetric ordered morphologies and even hybrid morphologies composed of A and C domains in different geometries. By constructing the triangular phase diagram of ABC triblock with fixed interaction parameters chi N-AB = chi N-BC = chi N-AC using self-consistent field theory, we predict a number of hybrid morphologies, including sphere-lamella, cylinder-lamella, perforated lamella-lamella, and sphere-cylinder. These hybrid morphologies exhibit relatively narrow stable regions as well as simple arrangements of A/C-domains. Furthermore, an interesting class of hybrid morphologies composed of spheres and network is absent, whose absence is mainly caused by the limited regions of sphere-containing hybrid morphologies. Accordingly, we introduce a topological asymmetry by branching BC-blocks at the A/B junction, forming an A(BC)(m) miktoarm star copolymer. In the phase diagram of A(BC)(2) we predict three interesting sphere-network hybrid morphologies in considerable regions, including sphere-diamond (SD), spheres within the double-gyroid networks, and sphere-perforated lamella. A stable SD over a sphere-gyroid is in striking contrast to stable alternating gyroids over alternating diamonds. When m = 2 is increased to m = 3, another new sphere-network morphology, that is, spheres within the double-diamond networks, is predicted in a considerable region. In addition, we find that the stability regions of these interesting sphere-network hybrid morphologies only shift slightly when chi N-AB = chi N-BC = chi N-AC is changed to chi N-AB = chi N-BC << chi N-AC. In brief, our work demonstrates that the combination of compositional asymmetry and topological asymmetry provides an opportunity for the fabrication of novel hybrid morphologies.